(this document is updated as the weeks proceed)

Week 7: Stats and studies: Correlation and causation

Week 8

Week 9

Arguments and logic, Weeks 9-10

We’re going to go back and forth between bare-bones examples and arguments from the wild, giving you more and more tools to deal with the real-world ones.

Arguments and reasoning in the wild, Weeks 11-13

Week 11

Fallacies.

Week 12

Week 13

Having an argument can extremize both sides

Taking a specific criticism as a general one

Don’t leave your shoes in the middle of the floor

You always leave your shoes in the middle of the floor

Avoiding entering argument mode

Daniel Pink on How to Persuade Others with the Right Questions

This guy

I’m not one of those people who went into psychology because they wanted to deal with feelings

What I’m into is evidence, reasons and logic. But I’ve learned I can only have those conversations with certain people if I deal with their feelings.

Probably won’t get to the below

Base rates, probabilities, and correlations

  • How probabilities are presented
  • Probabilities versus frequencies
    • When you hear a probability, think of 100 or 1000 cases
  • Correlations seemingly implied by rates
    • Which bits of the contingency table are given by a particular statement?

Is there a correlation between being male and liking avocados?

Suppose we learn that most males like avocados and also that most people who like avocadoes are male. Can we conclude that liking avocadoes is correlated with being male? It’s tempting to think the answer is “yes.” Understanding why that’s the wrong answer is crucial to having a full understanding of correlation.

For two dichomotous variables like male/female and liking avocados versus not, a positive correlation would mean that a higher proportion of males like avocado than females.

We know two things * Most males like avocado * Most people who like avocado are male

To establish a correlation, what we need to know is whether males like avocados at a higher rate than females do. But that simply does not follow from the fact that most males like avocados and most who like avocado are male. Look at this example:

Number of males versus females who like and don’t like avocados
Like Avocado Male Female
No 40 38
Yes 60 58

Most males in this example

What proportion of males like avocados? What proportion of females like avocados

  • Most people in the world like avocados. So we should expect most males to like avocados even if the same proportion of males and females like avocados.

  • Most people in the world are male (by a small amount). So we should expect most avocado eaters to be male even if males and females like avocados at the same rate.

    Putting these two facts together still doesn’t give us a correlation, because they could both be true even if males and females own cell phones at the same rate.  - Make a 2 x 2 table. For base rate of each - being male and owning a cellphone.

Most northern Hemisphere residents have above world average income. Most people with above world average income are in the northern hemisphere.

Most N. Hemisphere countries have more than 300 COVID-19 deaths. Most countries with more than 300 COVID-19 deaths are in the Northern Hemisphere. Is there a correlation between being in the N. Hemisphere and having more than 300 COVID-19 deaths? Maybe not, because most countries are in the N. Hemisphere anyway, so the second statement doesn’t tell us much. We need more to know whether the proportion of northern hemisphere countries with >300 COVID-19 deaths is greater than the proportion of southern hemisphere countries.

    - Another kind of mistake is simply that we fail to think proportionally. For example, suppose we've only observed John when it's cold and we notice that he has worn a hat 70% of the time. Can we conclude that there is a correlation in our observations between his wearing a hat and cold temperatures? Of course not! What if he wears a hat 70% of the time regardless of the temperature? In that case, there is no special correlation between his hat wearing and the cold: he just loves wearing hats.
    
    If we are told, "Most of the time when it's cold, John wears a hat," it's easy to forget that this is not enough to establish a correlation. To infer a correlation, we have to assume that John does not wear a hat most of the time on other days too . Maybe this is a safe assumption to make, but maybe not. The point is that if we just ignore it, we are neglecting the base rate, a mistake we encountered in the previous chapter. 

Learning from mistakes

those really were the droids you were looking for

those really were the droids you were looking for

  • This stormtrooper has realized that he made a big mistake. That’s good because then he can learn from the mistake.

The knew-it-all-along effect

Related to not wanting to admit that one is wrong.

divorced

divorced

This guy

  • In retrospect thinks he knew it all along
  • The observers are skeptical. They are probably right that he didn’t predict this.
  • But in retrospect, people think that they did predict something.
  • He didn’t predict it, so the best thing to do is realize his error, like the stromtrooper, so he can potentially learn from it
  • If one doesn’t know one made an error, one won’t learn much from the error. And wrong theories of the world never get fixed!

“I knew he would win!”

Prior to the 2012 election, average person said likelihood of Obama winning was 59%.

After the election, the average person (different set of people) said 68% (p < .001).

Hindsight bias

Ulkumen, Tannnenbaum, & Fox

Pundits carry on thinking all their political theories are correct.

Kahan has shown that evoking curiousity can help. Use it on yourself, too - I’m curious why you feel that way.

Survivorship * Bruce’s slide #132 * Famous people are usually very good, but also very lucky * “Failure to look for what is missing is a common shortcoming” https://youarenotsosmart.com/2013/05/23/survivorship-bias/ covers Wald, * Heuristic: Chesterton’s fence, as selection bias?